This invention relates to electronic chip fabrication, and particularly to correction of masks used in chip fabrication.
Thin film integrated circuits (ICs), commonly called xe2x80x9cchipsxe2x80x9d or xe2x80x9cIC chipsxe2x80x9d, are fabricated by a photolithographic process by which a photographic mask is positioned adjacent a substrate, such as a wafer, for adding features to or subtracting features from the substrate. Thus, each mask defines a layer of material to be added to the substrate, or material to be removed from a layer already on a substrate. Typically, the mask is used with another material, such as a photoresist, which is exposed by light through the image on the photographic mask to define the feature being formed on the substrate to form the chip. The feature is then deposited onto, or etched from, a layer on the substrate forming the chip.
The density of features on a chip is, in part, limited by the size of the photographic image of the mask. However, diffraction of light waves during photographic imaging introduces distortion in the resulting shapes of features on the substrate. A technique known as optical proximity correction (OPC) permits compensation of distortion due to diffraction of light waves by altering the mask into a distorted shape so that it will form the correct shape of the feature on the substrate. Using OPC, the features formed on the substrate may be smaller and more closely packed (dense) without forming breaks or shorts in the circuitry.
OPC is an iterative technique by which a computer model of process light intensity is applied to a computer model of a mask to identify the expected shape of a resulting wafer feature. The model mask is distorted through successive iterations until a mask model is derived that will produce features on actual wafers more closely replicating the desired wafer features. Existing OPC techniques require considerable time and consequently are expensive. Accordingly, there is a need for an improved technique to form shapes on a mask that, when light diffracts through the mask, produces a close approximation of the desired shape for the feature on the substrate.
One aspect of the present invention is a process for designing a mask for use in a photolithographic process to offset the effects of light diffraction. At least one region, having a length, is identified along each edge of a mask feature. A matrix is derived containing a plurality of contribution of movement factors, each representing the contribution to light amplitude due to movement of the respective region normal to the region. The movement for each region is a solution of the matrix.
In one embodiment, the matrix is derived by identifying an amplitude curve associated with distance from a center of a disk of light. The length of each line between a midpoint R of each region and each of a plurality of points W along edges of the mask feature are identified. A plurality of contributions of movement factors are derived, each based on the amplitude curve, the length of the respective line and the size of the disk of light. The matrix of the contributions of movement is derived from the plurality of contribution of movement factors.
In preferred embodiments, the movement of each region is defined by calculating an error amplitude for each point W along edges of the mask feature. A plurality of linear expressions are derived from the matrix and a cost function is derived for each point W based on the respective linear expression and an error value. The amount that a region is to be moved is based on minimizing a cost function.
In preferred embodiments, the cost function is derived by subtracting the error value for each point W from the respective linear expression to identify a discrepancy for each point. The value of the discrepancy is symbolically squared. The movement for the region is calculated by deriving       ∂    F        ∂    V  
for each region, where F is the cost function and V is the amount of movement of the respective region. The value of V is calculated for each region based on a solution of all equations             ∂      F              ∂      V        =  0.
Also preferably, the cost function is optimized by adding correction terms for additional optimization goals to the cost function.
In preferred embodiments, the error amplitude is derived from a light amplitude for each point W and a target light intensity.
Preferably, the amount of movement is adjusted for each region whose area of movement may be affected by movement of an adjacent region. One technique for adjusting the amount of movement includes calculating the area of movement of one region based on the length of that region and its amount of defined movement. Changes in area of movement of that region due to movement of regions adjacent that region are identified. The amount of movement of that region is adjusted so that the area moved equals the calculated area.
According to another aspect of the invention, a computer useable medium contains a computer readable program comprising code that causes a computer to correct mask definitions for the effects of light diffraction.